Prescribed-Time Stabilization of Singularly Perturbed Systems
Yan Lei, Yan‐Wu Wang, Xiao‐Kang Liu, Wu Yang
Abstract
Dear Editor, This letter investigates the prescribed-time stabilization of linear singularly perturbed systems. Due to the numerical issues caused by the small perturbation parameter, the off-the-shelf control design techniques for the prescribed-time stabilization of regular linear systems are typically not suitable here. To solve the problem, the decoupling transformation techniques for time-varying singularly perturbed systems are combined with linear time-varying high gain feedback design techniques. A composite linear time-varying state feedback controller is designed, and the existence of the time-varying Chang transformation matrix for decoupling the slow and fast dynamics is guaranteed. As a result, the prescribed-time stability is ensured. Finally, a numerical example is provided to illustrate the effectiveness of the results.